Final answer:
Societies settled along river valleys like the Nile and Tigris and Euphrates around 4000 B.C.E., initiating the rise of early civilizations in these fertile areas.
Step-by-step explanation:
The river valley cultures, such as those near the Tigris and Euphrates in Mesopotamia and the Nile delta of Egypt, began their shift from the uplands to these fertile river valleys rich in soils due to river deposits quite early in human history. It has been well-documented that these regions, part of the Fertile Crescent, witnessed the development of early civilizations during the fourth millennium BCE, with Mesopotamia specifically being referred to as the Cradle of Civilization. Given the options provided, the correct period for when societies began establishing themselves in these river valleys would be A) 4000 B.C.E., as this time frame corresponds to the rise of such early civilizational attributes as the development of agriculture, the construction of irrigation systems, and the emergence of rulers and specialized artisans.